Transient Beam Loading Research Articles

Implementation of the beam-loading effect in the tracking code RF-track based on a power-diffusive model

The need to achieve high energies in particle accelerators has led to the development of new accelerator technologies, resulting in higher beam intensities and more compact devices with stronger accelerating fields. In such scenarios, beam-loading effects occur, and intensity-dependent gradient reduction affects the accelerated beam as a consequence of its interaction with the surrounding cavity. In this study, a power-diffusive partial differential equation is derived to account for this effect. Its numerical resolution has been implemented in the tracking code RF-Track, allowing the simulation of apparatuses where transient beam loading plays an important role. Finally, measurements of this effect have been carried out in the CERN Linear Electron Accelerator for Research (CLEAR) facility at CERN, finding good agreement with the RF-Track simulations.

Beam Loading Compensation of Traveling Wave Linac to a Multi-bunch Pulse with Gaps

In the electron driven ILC (International Linear Collider) positron source, the beam is generated and accelerated in a multi-bunch format with mini-trains. The macro-pulse contains 2 to 4 mini-trains with several gaps, because the pulse format is a copy of a part of the bunch storage pattern in DR (Damping Ring). This pulse format causes a variation of the accelerator field in the pulse due to the transient beam loading and an intensity fluctuation of captured positron. The beam loading is compensated by amplitude modulation on the input RF in the positron booster composed from L-band and S-band traveling wave RF cavity. In this article, we derive the exact solution for the compensation with the gaps. In addition, we evaluate the effect of the time constant (delay) of the input RF modulation due to klystron Q-value.

Periodic transient beam loading effect with passive harmonic cavities in electron storage rings

In our previous study of bunch lengthening for the planned Hefei Advanced Light Facility (HALF) storage ring, a periodic transient beam loading effect was found in the presence of passive harmonic cavities for some cases, which can dramatically affect the bunch lengthening as well as the beam stability [T. L. He et al., Bunch lengthening of the HALF storage ring in the presence of passive harmonic cavities, in Proceedings of the IPAC2021, Campinas, SP (JACoW, Campinas, SP, Brazil, 2021), pp. 2082--2085, TUPAB265]. In this paper, we continue to use HALF as an example, via both tracking simulation and semianalytical calculation, to comprehensively study the characteristics of this periodic transient effect, analyze its dependence on some relevant factors and investigate the impact of fill pattern on its periodicity. It is found that there exits a threshold current for this periodic transient effect, which can be increased by the reduction of $R/Q$ of harmonic cavity (HC) and the increase of main cavity (MC) voltage, HC detuning, momentum compaction, and energy spread, as well as the inclusion of short-range wake. In addition, the periodicity of bunch centroid oscillation can be affected by the damping time and MC beam loading, and completely interrupted due to the nonuniform fill pattern, but this is not helpful for improvement of bunch lengthening.

Application of a modified iterative learning control algorithm for superconducting radio-frequency cavities

Transient beam loading, which causes cavity gradient fluctuation, is becoming a major concern for the stable operation of the high current superconducting radio-frequency (SRF) accelerators. Iterative learning control (ILC) is an effective algorithm aiming to improve systems operated in repetitive mode. This ILC technique was successfully introduced to the low-level radio-frequency (LLRF) control in accelerators to compensate for the field fluctuation caused by repetitively pulsed beam. The modern LLRF system prefers to use the FPGA-based hardware platform to realize a real-time control framework. However, considering the algorithm complexity and the hardware cost, the ILC algorithm is usually implemented outside FPGA. This practice would decrease the real-time ability of the control system. In this paper, we present a modified ILC algorithm that can be implemented inside FPGA. The key idea of our method is to simplify the beam profile using a rectangular pulse. The method was demonstrated in the SRF cavities at Chinese Accelerator driven system Front-end demo SRF linac (CAFe). The experimental results in the CAFe beam-commissioning confirmed that the beam-induced gradient fluctuation is successfully suppressed.

Graphics-processing-unit-accelerated simulation for longitudinal beam dynamics of arbitrary bunch trains in electron storage rings

We propose a novel algorithm to deal with the interaction of beam-cavity, which is convenient to be implemented on the platform of matlab supporting graphics process unit operations and can significantly improve the computational efficiency. Actually, this algorithm has been implemented and the corresponding code is named stable, which can be used to study the longitudinal beam dynamics of arbitrary filled bunches in electron storage rings. In this paper, the stable code is mainly used to evaluate the bunch lengthening produced by the passive higher harmonic cavity. We first carry out efficiency tests for stable and the results are satisfactory. We then benchmark the stable code against the semianalytical approach and elegant tracking for equilibrium and nonequilibrium cases, respectively, and the results are in good agreement. Furthermore, the stable code is applied to the case of Advanced Light Source upgrade (ALS-U) with distributed gaps, and the results firstly reveal a regular and periodic transient beam loading effect and thus show a nonequilibrium state for the overstretching case. As a second example, the stable code is also applied to the case of the Hefei advanced light facility (HALF) storage ring with uniformly distributed gaps, and the results show that the passive normal conducting harmonic cavities with a total $R/Q$ of $\ensuremath{\sim}200\text{ }\text{ }\mathrm{\ensuremath{\Omega}}$ will cause severe transient effects, thus being not suitable for Hefei advanced light facility.

Transient Beam Loading in the CBETA Multi-Turn ERL

Transient Beam Loading in the CBETA Multi-Turn ERL

A new beam synchronous processing architecture with a fixed frequency processing clock. Application to transient beam loading compensation in the CERN SPS machine

New projects being implemented or planned at CERN, such as the LHC Injectors Upgrade (LIU), the High-Luminosity LHC (HL-LHC) or the Future Circular Collider (FCC), motivate the change of several architectural paradigms in the Low Level RF systems (LLRF). In the upgraded Super Proton Synchrotron (SPS) LLRF, the distribution of RF, the revolution frequency, settings and synchronization timings will rely on a deterministic link, the White Rabbit (WR), exploiting a distributed topology. The digital electronics (FPGA) will now use a fixed frequency clock extracted locally in each node from this data stream. The paper presents a new solution for algorithms that treat beam-induced perturbations as they must solve the challenge to tune their processing to the instantaneous revolution frequency, Beam Synchronous Processing (BSP). We use dynamic resampling of uniform sampled data as tuning element between a sweeping spectrum and the static processing implemented with fixed frequency clocks. The paper applies the novel Beam Synchronous Processing method to transient beam loading compensation. It presents a One Turn delay FeedBack (OTFB) for the SPS based on a cascade of two variable ratio resamplers.

P.445 Dose-response relationships of antipsychotic drugs for major depressive disorder: a systematic review and meta-analysis

New projects being implemented or planned at CERN, such as the LHC Injectors Upgrade (LIU), the High-Luminosity LHC (HL-LHC) or the Future Circular Collider (FCC), motivate the change of several architectural paradigms in the Low Level RF systems (LLRF). In the upgraded Super Proton Synchrotron (SPS) LLRF, the distribution of RF, the revolution frequency, settings and synchronization timings will rely on a deterministic link, the White Rabbit (WR), exploiting a distributed topology. The digital electronics (FPGA) will now use a fixed frequency clock extracted locally in each node from this data stream. The paper presents a new solution for algorithms that treat beam-induced perturbations as they must solve the challenge to tune their processing to the instantaneous revolution frequency, Beam Synchronous Processing (BSP). We use dynamic resampling of uniform sampled data as tuning element between a sweeping spectrum and the static processing implemented with fixed frequency clocks. The paper applies the novel Beam Synchronous Processing method to transient beam loading compensation. It presents a One Turn delay FeedBack (OTFB) for the SPS based on a cascade of two variable ratio resamplers.

Harmonic-cavity stabilization of longitudinal coupled-bunch instabilities with a nonuniform fill

In synchrotrons, nonuniform fill patterns, which give rise to beam phase transients and a spread in synchrotron tune between bunches, have been observed to damp longitudinal coupled-bunch instabilities driven by higher-order modes in rf cavities. The transients are especially large in the presence of Landau cavities, which are used commonly in storage-ring light sources and particularly in the new generation of diffraction-limited storage rings. A method has recently been devised to predict the beam transient including complex form factors for the different bunches. This has now been extended to accurately predict the growth-rates and oscillation frequencies of coupled-bunch modes for arbitrary fill patterns, taking the individual complex form factors and equilibrium phases of the different bunches into account. In this paper, the extended method is presented and the theory is outlined. For a case with significant transient beam loading, predictions of the resulting beam transient and bunch profiles are compared to measurements. Predictions of coupled-bunch mode behavior are then benchmarked against results from the macroparticle tracking code mbtrack with good agreement. Finally, the method is used to predict the behavior of coupled-bunch modes as a function of the fields in passive Landau cavities.

Beam loading effects and microwave instability in the booster ring of a high intensity heavy-ion accelerator facility

Transient beam loading effects and microwave instability are very important in ion synchrotrons. A simulation code longitudinal particle tracking code (LPTC) based on multiparticle tracking is developed to simulate the beam loading effects and the longitudinal beam instabilities in the booster ring (BRing) of the High Intensity heavy-ion Accelerator Facility (HIAF). A process of beam capture, acceleration, debunching, and the second capture is simulated with a reference ion beam of ${^{78}\mathrm{Kr}}^{19+}$. The simulation results show that the beam loading effects have major contribution to the beam behavior during the debunching stage and the second capture stage. A feed-forward system is suggested to compensate the beam loading effects, and the main parameters of the feed-forward system are given. The microwave instability of coasting ${^{78}\mathrm{Kr}}^{19+}$ beams is observed from the simulation results. The threshold of the microwave instability is also given. The development of self-bunching and methods to suppress the microwave instability in the BRing are discussed.

SHORT PULSE ELECTRON LINAC WITH FULL BEAM LOADING COMPENSATION

Acceleration of intense short-pulsed electron beams in transient mode with energy spread about a few tenths of a percent is the actual problem for RF linacs, in an instance, for an electron injector of a storage ring. In this work we study both analytically and numerically unsteady self-consistent beam dynamics in the one section RF linac fed from SLED. For compensation of the transient beam loading, resulting in beam energy spread, a method of a beam delay with respect to RF pulse is consider. In order to increase efficiency of this method we choose a homogenous dick-loaded waveguide with π/2 phase advance as an accelerating structure that characterized by the minimal frequency dispersion of group velocity. The preliminary results show that the full beam loading compensation is possible for the 1.2 A beam at its acceleration up to 60 MeV during 50 ns.

Transient beam loading and rf power evaluation for future circular colliders

Interaction of the beam with the fundamental impedance of the accelerating cavities can limit the performance of high-current accelerators. It can result in a significant variation of bunch-by-bunch parameters (bunch length, synchronous phase, etc.) if filling patterns contain gaps that are not negligible compared with the cavity filling time. In the present work, this limitation is analyzed using the steady-state time-domain approach for the high-current option (Z) of the future circular electron-positron collider and for the future circular hadron-hadron collider. Mitigation of transient beam loading by direct rf feedback is addressed with evaluation of additional required generator power.

Transient Beam Loading and Mitigation in JLEIC Collider Rings

Transient Beam Loading and Mitigation in JLEIC Collider Rings

Transfer function measurement for the SSRF SRF system

A digital transfer function measurement system has been embedded in the low-level radio frequency (LLRF) system of the storage ring of the Shanghai Synchrotron Radiation Facility. The measurement results indicate that the decreased control accuracy at high current is primarily owing to ripples from the high-voltage power supply, the transient beam loading effect, and the digital aliasing effect. The current LLRF algorithm is not able to suppress these disturbances.

Design of CEPC superconducting RF system

CEPC is a 100-km double-ring circular electron–positron collider operating at 90–240 GeV center-of-mass energy of Z-pole, WW-pair production threshold and Higgs resonance. The conceptual design report (CDR) of CEPC has been published as an important step to move the project forward. The superconducting RF (SRF) system is one of the most important and challenging accelerator systems due to the wide range of beam energy and current. In this paper, the layout, parameters and configuration of the superconducting RF system for the CEPC collider ring will be introduced. Issues of beam cavity interactions including transient beam loading and coupled-bunch instabilities of accelerating mode are discussed.

Performance of an electron linear accelerator for the first photoneutron source in China

A compact 15.0-MeV, 1.5-kW electron linear accelerator (LINAC) was successfully constructed to provide an electron beam for the first photoneutron source at the Shanghai Institute of Applied Physics, Shanghai, China. This LINAC consists of five main parts: a thermal cathode grid-controlled electron gun, a pre-buncher, a variable-phase-velocity buncher, a light-speed accelerating structure, and a high-power transportation beamline. A digital feedforward radio frequency compensator is adopted to reduce the energy spread caused by the transient beam loading effect. Furthermore, a real-time electron gun emission feedback algorithm is used to keep the beam stable. After months of efforts, all the beam parameters successfully met the requirements of the facility. In this paper, the beam commissioning process and performance of the LINAC are presented.

Self-consistent calculation of transient beam loading in electron storage rings with passive harmonic cavities

The ongoing trend towards synchrotron light storage rings with ultralow emittance lattices leads to greater challenges to achieve beam stability, sufficient Touschek lifetime, low heating of machine components, and conservation of the emittance at high bunch charge. One solution to meet these challenges is to lengthen the electron bunches with harmonic cavities. Many upgrade proposals therefore include harmonic cavities to enhance the machine performance. This is also the case for the MAX IV 3 GeV storage ring, which employs passive third harmonic cavities to achieve up to five times bunch lengthening. Unfortunately, the performance of the harmonic cavities is reduced if a gap in the fill pattern is required. In this paper, the effect on synchronous phase and bunch length due to a gap in the fill pattern for rings with passive harmonic cavities is calculated in a self-consistent way including the bunch form factor. The aim is to achieve faster simulation of various schemes for compensating a gap compared to multiparticle tracking. A new semianalytical method based on an iterative matrix formulation is presented, as well as a single-particle tracking code including the bunch form factor. The results from these methods are compared to both results from a multiparticle tracking code and measurements at the MAX IV 3 GeV storage ring. The importance of including the bunch form factor in simulations is evaluated and discussed.

Compensation of Transient Beam Loading in Ramping Synchrotrons using a Fixed Frequency Processing Clock

Transient beam loading compensation schemes, such as One-Turn-FeedBack (OTFB), require beam synchronous processing (BSP). Swept clocks derived from the RF, and therefore harmonic to the revolution frequency, are widely used in CERN synchrotrons; this simplifies implementation with energy ramping, where the revolution frequency changes. It is however not optimal for state-of-the-art digital hardware that prefers fixed frequency clocks. An alternative to the swept clocking is the use of a deterministic protocol, for example White Rabbit (WR): a fixed reference clock can be extracted from its data stream, while enabling digital distribution of the RF frequency among other data. New algorithms must be developed for BSP using this fixed clock and the digital data transmitted on the WR link. This is the strategy adopted for the SPS Low Level RF (LLRF) upgrade. The paper gives an overview of the technical, technological and historical motivations for such a paradigm evolution. It lists the problems of fixed clock BSP, and presents an innovative solution based on a real-time variable ratio re-sampler for implementing an OTFB with the new fixed clock scheme.

Compensation of transient beam loading in ramping synchrotrons using a fixed frequency processing clock

Transient beam loading compensation schemes, such as One-Turn-FeedBack (OTFB), require beam synchronous processing (BSP). Swept clocks derived from the RF, and therefore harmonic to the revolution frequency, are widely used in CERN synchrotrons; this simplifies implementation with energy ramping, where the revolution frequency changes. It is however not optimal for state-of-the-art digital hardware that prefers fixed frequency clocks. An alternative to the swept clocking is the use of a deterministic protocol, for example, White Rabbit (WR): a fixed reference clock can be extracted from its data stream, while enabling digital distribution of the RF frequency among other data. New algorithms must be developed for BSP using this fixed clock and the digital data transmitted on the WR link. This is the strategy adopted for the SPS Low Level RF (LLRF) upgrade. The paper gives an overview of the technical, technological and historical motivations for such a paradigm evolution. It lists the problems of fixed clock BSP, and presents an innovative solution based on a real-time variable ratio re-sampler for implementing an OTFB with the new fixed clock scheme.

Transient Beam Loading Due to the Bunch Train Gap and Its Compensation Experiments at BEPC-II and ALS

Transient Beam Loading Due to the Bunch Train Gap and Its Compensation Experiments at BEPC-II and ALS